diff --git a/pyproject.toml b/pyproject.toml
index 4a0d77d2d..af1a9cee6 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -31,7 +31,7 @@ license-files = ["LICENSE", "AUTHORS"]
 dependencies = [
   "borghash ~= 0.1.0",
   "borgstore ~= 0.3.0",
-  "msgpack >=1.0.3, <=1.1.0",
+  "msgpack >=1.0.3, <=1.1.1",
   "packaging",
   "platformdirs >=3.0.0, <5.0.0; sys_platform == 'darwin'",  # for macOS: breaking changes in 3.0.0,
   "platformdirs >=2.6.0, <5.0.0; sys_platform != 'darwin'",  # for others: 2.6+ works consistently.
diff --git a/src/borg/helpers/msgpack.py b/src/borg/helpers/msgpack.py
index b6144a899..e669e9014 100644
--- a/src/borg/helpers/msgpack.py
+++ b/src/borg/helpers/msgpack.py
@@ -209,7 +209,7 @@ def is_supported_msgpack():
 
     if msgpack.version in []:  # < add bad releases here to deny list
         return False
-    return (1, 0, 3) <= msgpack.version <= (1, 1, 0)
+    return (1, 0, 3) <= msgpack.version[:3] <= (1, 1, 1)
 
 
 def get_limited_unpacker(kind):